Solve for $x$ and $y$ using elimination. $\begin{align*}-4x-9y &= 6 \\ -5x-4y &= -7\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-5$ and the bottom equation by $4$ $\begin{align*}20x+45y &= -30\\ -20x-16y &= -28\end{align*}$ Add the top and bottom equations. $29y = -58$ Divide both sides by $29$ and reduce as necessary. $y = -2$ Substitute $-2$ for $y$ in the top equation. $-4x-9( -2) = 6$ $-4x+18 = 6$ $-4x = -12$ $x = 3$ The solution is $\enspace x = 3, \enspace y = -2$.